How long do the flowers of a Christmas Cactus last?

I received a Christmas cactus about 2 1/2 weeks ago with some buds just starting and some buds almost all the way open. Since then, most of the flowers have bloomed beautifully, but about a week after the flower blooms, the flower itself starts to wilt and shrivel. Is this normal? The rest of the plant looks healthy, it's just the flowers that are starting to shrivel up after blooming. If this is normal, should I pinch off the wilting flowers or just leave it alone?